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Time-reversal invariant (TRI) Dirac and Weyl semimetals in three dimensions(3D) can host open Fermi arcs and spin-momentum locking Fermi loops on thesurfaces. We find that when they become superconducting with $s$-wave pairingand the doping is lower than a critical level, straight $\pi$-flux vortex linesterminating at surfaces with Fermi arcs or spin-momentum locking Fermi loopscan realize 1D topological superconductivity and harbor Majorana zero modes attheir ends. Remarkably, we find that the vortex-generation-associated Zeemanfield can open (when the surfaces have only Fermi arcs) or enhance thetopological gap protecting Majorana zero modes, which is contrary to thesituation in superconducting topological insulators. By studying the tiltingeffect of bulk Dirac and Weyl cones, we further find that type-I Dirac and Weylsemimetals in general have a much broader topological regime than type-II ones.Our findings build up a connection between TRI Dirac and Weyl semimetals andMajorana zero modes in vortices.

Vortex end Majorana zero modes in superconducting Dirac and Weyl semimetals